For 3D animation Bézier curves are often used to define 3D paths as well as 2D curves for keyframe interpolation.

For 2D vector animations, the rendering process is the key frame illustration process, while tweened frames are rendered as needed.

For 2D figures in general there are two more categories:

For curves that cannot be drawn on a 2D surface without self-intersections, the corresponding universal curve is the Menger sponge, a higher-dimensional generalization.

For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional ( 2D ) surface.

For these reasons, documents and illustrations are often stored or transmitted as 2D graphic files.

For hardware accelerated 3D and 2D acceleration on Linux, Mac OS X and DOS, AllegroGL and OpenLayer are available.

For example, in 2D cases, scene graphs typically render themselves by starting at the tree's root node and then recursively draw the child nodes.

For example, video cards with 3D accelerators ( most, ) have two voltage and clock rate settings, one for 2D and one for 3D, but were designed to operate with three voltage stages, the third being somewhere between the aforementioned two, serving as a fallback when the card overheats or as a middle-stage when going from 2D to 3D operation mode.

For example, at a time ten years before E, if we consider the set of all events in the past light cone of E which occur at that time, the result would be a sphere ( 2D: disk ) with a radius of ten light-years centered on the future position E will occur.

For example, 4-connectivity and 8-connectivity in 2D.

For 2D space and affine transform the basis is defined by a pair of points.

For example, a nearsighted person who needs a − 2. 0 diopter corrective lens will see something like the 2D image when viewing a standard eye chart at the standard 20-foot distance without glasses.

For 2D systems with one of the dimensions much larger than the other DMRG is also accurate, and has proved useful in the study of ladders.

For the first time with real player names by obtaining the FIFPro license, the PlayStation, PC, 32X and Sega Saturn versions used EA's " Virtual Stadium " engine, with 2D sprite players moving around a real-time 3D stadium.

For example, for the 1984 IBM PC / AT code 1D is issued when about to Determine Memory Size Above 1024K, and code 2D in the event of 8042 Keyboard Controller Failure, 105 System Error.

For the 2012 / 13 season, the new Málaga shirt will interact with the fans thanks to a 2D barcode, via which the blanquiazul faithful will receive, on their Smartphones, exclusive updates.

For a 2D + t dimensional case ( 3D or n-D cases are similar ) a voxel at location with intensity will have moved by, and between the two image frames, and the following image constraint equation can be given:

For example, to locate stocks in plottable 2D space based on their hi-D time-series shapes.

For example, a standard 24 bits per pixel, 1024 × 768 resolution, flat / 2D display requires about 135 MB / s to be sent to the display hardware to sustain 60 frames per second, whereas a 24 bits per voxel, 1024 × 768 × 1024 ( 1024 " pixel layers " in the Z axis ) volumetric display would need to send about three orders of magnitude more ( 135 GB / s ) to the display hardware to sustain 60 volumes per second.

For the most part, Davis appreciated the translation of the 3D from their 2D counterparts and the effects used for the spirit attacks.

For example, in one level, the player can find the Prince sitting on a photocopier, with Slip ( the Cousin who is a flat 2D clone of the Prince ) emerging from the paper tray.

For example, commercial stations such as Channel 5 are made available to viewers in the United Kingdom, but are restricted in the Republic of Ireland and northern France, even though these areas are covered by the same satellite footprint, Astra 2D.

For the present it is enough to note that in the grotesque figure of Jacoby, at the moment of his collapse, all these elements come together in prophetic parody.

For this reason, he appears as an independent and self-reliant figure, whose rugged individualism need not be pressed into the mold of a 9 to 5 routine.

For the figure of Vincent Berger Malraux has obviously drawn on his studies of T. E. Lawrence ( though Berger fights on the side of the Turks instead of against them ), and like both Lawrence and Malraux himself he is a fervent admirer of Nietzsche.

The new `` School For Wives '' was interpreted according to a principle that is becoming increasingly common in the playing of classic comedy -- the idea of turning some obviously ludicrous figure into a tragic character.

For a few innings the Anniston team couldn't figure him out.

For some adherents it represents a non-papal Catholicism, for others a form of Protestantism though without a dominant guiding figure such as Luther, Knox, Calvin, Zwingli or Wesley.

For example, letters 1, 5, and 8 contain a discussion on the question, whether the use of a piece of metal with the figure of a lion, as a talisman, is permitted by Jewish law for medicinal purposes, or is prohibited as idolatrous.

For flow through a tube with one inlet ( state 1 ) and exit ( state 2 ) as shown in the figure in this section, the continuity equation may be written and solved as:

For the same figure, a control volume analysis yields:

For example, the increase in rotational speed of a spinning figure skater as the skater's arms are contracted is a consequence of conservation of angular momentum.

For a uniform polyhedron, the face of the dual polyhedron may be found from the original polyhedron's vertex figure using the Dorman Luke construction.

For example, students have been found to perform better on a test of knowledge about a text passage when a second reading of the passage is delayed rather than immediate ( see figure ).

For example, suppose the word square is defined by " A figure is square if and only if it has four perpendicular sides of equal length.

For example, the fundamental group of the figure eight is the free group on two letters.

For this reason, astronomical position determination – measuring the direction of the plumbline by astronomical means – works fairly well provided an ellipsoidal model of the figure of the Earth is used.

Josephus related the Biblical figure Gomer to Galatia ( or perhaps to Gaul in general ): " For Gomer founded those whom the Greeks now call Galatians, but were then called Gomerites.

The red dot overtakes two green dots when moving from the left to the right of the figure. New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front. For surface gravity waves, the water particle velocities are much smaller than the phase velocity, in most cases.

For that he must pass from representing a single figure to several together ; history and myth must be depicted ; great events must be represented as by historians, or like the poets, subjects that will please, and climbing still higher, he must have the skill to cover under the veil of myth the virtues of great men in allegories, and the mysteries they reveal ".

For example, it had 100, 000 people in 1852 and then 250, 000 people in 1883 ; by 1901, the figure had doubled again to 500, 000.

For Christians, Moses — mentioned more often in the New Testament than any other Old Testament figure — is often a symbol of God's law, as reinforced and expounded on in the teachings of Jesus.

For example, suppose there are two bodies of equal mass, one stationary and one approaching the other at a speed ( as in the figure ).

For example, in a non-inverting amplifier ( see the figure on the right ) adding a negative feedback via the voltage divider R < sub > f </ sub >, R < sub > g </ sub > and the differential to single ended conversion is completed without gain losses.

For instance, it can be used so as to say that no person or historical figure fits the set of descriptions attributed to the person that goes by the name of " Moses ".

For example, see figure, in the US United States Department of Veterans Affairs ( VA ) the program management life cycle is depicted and describe in the overall VA IT PROJECT MANAGEMENT FRAMEwork to address the integration of OMB Exhibit 300 project ( investment ) management activities and the overall project budgeting process.